Compound Angle Formulas

Can someone describe to me clearly, how you would solve these questions:

1. Angles x and y are located in the first quadrant such that sinx=4/5 and cosy=7/25.
a) determine an exact value for cos x
b) determine an exact value for sin y
c) determine an exact value for sin(x+y)

2. angle x lies in the third quadrant, and tanx=7/24
a) determine an exact value for cos2x
b) determine an exact value for sin2x

for 1 a and b I got the answers, but for 1 c, I am not sure how to approach it

1) for sin(x) = 4/5
you can construct the triangle with opposite length 4 and hypotenuse 5. you can find angle x using sin^-1. then find the adjacent side and find cos(x).
use similar methods for part b. use double angle forumla for part c.

Trig Ratios

Hello skeske

Originally Posted by skeske1234

Can someone describe to me clearly, how you would solve these questions:

1. Angles x and y are located in the first quadrant such that sinx=4/5 and cosy=7/25.
a) determine an exact value for cos x
b) determine an exact value for sin y
c) determine an exact value for sin(x+y)

This is what you need to know to solve a question like this:

If an angle is in the first quadrant, then its sine and cosine are both positive.

The relation between sine and cosine is

So:

, since

In the same way, if

Originally Posted by skeske1234

for part c of question 1, if I get to
sin(4/5)cos(7/25)+cos(3/5)sin(24/25)
what do I do next?

You're getting things a bit confused here.

2. angle x lies in the third quadrant, and tanx=7/24
a) determine an exact value for cos2x
b) determine an exact value for sin2x

If angle lies in the third quadrant, then and are both negative.

If you know the value of , then use:

and then use

Then,

Finally, for , the quickest way is to use

Note that will be positive, since and are both negative and

Can you complete this? If not, let's see your working, and we'll finish it for you.